The multi‐stage centred‐scheme approach applied to a drift‐flux two‐phase flow model

Abstract

SUMMARYFor two-phase ow models, upwind schemes are most often di cult do derive, and expensive to use. Centred schemes, on the other hand, are simple, but more dissipative. The recently proposed multistage (MUSTA) method is aimed at coming close to the accuracy of upwind schemes while retaining the simplicity of centred schemes. So far, the MUSTA approach has been shown to work well for the Euler equations of inviscid, compressible single-phase ow. In this work, we explore the MUSTA scheme for a more complex system of equations: the drift-ux model, which describes one-dimensional two-phase ow where the motions of the phases are strongly coupled. As the number of stages is increased, the results of the MUSTA scheme approach those of the Roe method. The good results of the MUSTA scheme are dependent on the use of a large-enough local grid. Hence, the main beneÿt of the MUSTA scheme is its simplicity, rather than CPU-time savings.

Weak Solutions for a Gas-Liquid Model Relevant for Describing Gas-Kick in Oil Wells

“…The starting point for the investigations of this work is a one-dimensiional two-phase model of the drift-flux type. This model is frequently used to simulate unsteady, compressible flow of liquid and gas in pipes and wells [1,2,4,5,6,15,18,20,21,25,22,10]. The model consists of two mass conservation ec|uations corresponding to each of the two phases, gas {g) and liquid (/), and one eciuation for the conservation of the momentum of the mixture.…”

“…More details will be given in section 2. We refer also to [5,6,10,18,20,21,22,25] for various numerical schemes which have been developed for the study of the drift-fiux model.…”

A Robust and accurate Riemann solver for a compressible two-phase flow model

“…This test case is the simplest Riemann problem that was originally presented in [31] and investigated in [27,32,33]. Results are displayed in Fig.…”

Splitting methods for relaxation two-phase flow models

“…Increase m and by one repeat from step 1. In the numerical simulations presented in the numerical results section, a MUSTA 2-2 method (M = N = 2) will be used, with 4 local grid cells and 2 local time steps, similar to the one described by Munkejord et al (2006).…”